No description available.

No description available.

No description available.

No description available.

No description available.

In end-stage kidney disease, kidneys no longer sufficiently perform their intended functions, for example, filtering blood of excess fluid and waste products. Without transplantation or chronic dialysis, this condition results in mortality. Dialysis is the process of artificially replacing some of the kidney’s functionality by passing blood from a patient through an external semi-permeable membrane to remove toxins and excess fluid. The rate of ultrafiltration – the rate of fluid removal from blood – is controlled by the hemodialysis machine per prescription by a nephrologist. While essential for survival, hemodialysis is fraught with clinical challenges. Too high a fluid removal rate could result in hypotensive events where the patient blood pressure drops significantly which is associated with adverse symptoms such as exhaustion, fainting, nausea, and cramps, leading to decreased patient quality of life. Too low a fluid removal rate, in contrast, could leave the patient fluid overloaded often leading to hypertension, which is associated with adverse clinical outcomes. Previous work in our lab demonstrated via simulations that it is possible to design an individualized, model-based ultrafiltration profile with the aim of minimizing hypotensive events during dialysis. The underlying model using in the design of the individualized ultrafiltration profile is a simplified, linearized, continuous-time model derived from a nonlinear model of the patient’s fluid dynamics system. The parameters of the linearized model are estimated from actual patient’s temporal hematocrit response to ultrafiltration. However, the parameter identification approach used in the above work was validated using limited clinical data and often failed to achieve accurate estimation. Against this backdrop, this thesis had three goals: (1) obtain a new, larger set of clinical data, (2) improve the linearized model to account for missing physiological aspects of fluid dynamics, and (3) develop and validate a new approach for identification of model parameters for use in the design of individualized ultrafiltration profiles. The first goal was accomplished by retrofitting an entire in-center, hemodialysis clinic in Holyoke, MA, with online hematocrit sensors (CliC devices), Wi-Fi boards, and a laptop with a radio receiver. Treatment data was wirelessly uploaded to a laptop and redacted files and manual treatment charts were made available for our research per approved study IRB. The second goal was accomplished by examining the nonlinear system of equations governing the relevant dynamics and simplifying the model to an identifiable case. Considerations of refill not accounted for fully in previous works were integrated into the Cardimino 7 linearized model, adding terms but making it generally more accurate to the underlying dynamics. The third goal was accomplished by developing an algorithm to identify major system parameters, using steady-state behavior to effectively reduce the number of parameters to identify. The system was subsequently simulated over an established range for all remaining parameters, compared to collected data, with the lowest RMS error case being taken as the set of identified parameters. While intra-patient identified individual model parameters were associated with a high degree of variability, the system’s steady-state gain and time constants exhibited more consistent estimations, though the time constants still had high variability overall. Parameter sensitivity analysis shows high sensitivity to small changes in individual model parameters. The addition of refill dynamics in the model constituted a significant improvement in the identifiability of the measured dynamics, with up to 70% of data sets resulting in successful estimates. Unmodelled dynamics, resulting from unmeasured input variables, resulted in about 30% of measured data sets unidentifiable. The updated model and associated parameter identification developed in this thesis can be readily integrated with the model-based design of individualized UFR profile.

Controlling infectious disease spread and preventing disease onset are ongoing challenges, especially in the presence of newly emerging diseases. While vaccines have successfully eradicated smallpox and reduced occurrence of many diseases, there still exists challenges such as fear of vaccination, the cost and difficulty of transporting vaccines, and the ability of attenuated viruses to evolve, leading to instances such as vaccine derived poliovirus. Antibiotic resistance due to mistreatment of antibiotics and quickly evolving bacteria contributes to the difficulty of eradicating diseases such as tuberculosis. Additionally, bacteria and fungi are able to produce an extracellular matrix in biofilms that protects them from antibiotics/antifungals. Mathematical models are an effective way of measuring the success of various control measures, allowing for cost savings and efficient implementation of those measures. While many models exist to investigate the dynamics on a human population scale, it is also beneficial to use models on a microbial scale to further capture the biology behind infectious diseases. In this dissertation, we develop mathematical models at several spatial scales to help improve disease control. At the scale of human populations, we develop differential equation models with quarantine control. We investigate how the distribution of exposed and infectious periods affects the control efficacy and suggest when it is important for models to include realistically narrow distributions. At the microbial scale, we use an agent-based stochastic spatial simulation to model the social interactions between two yeast strains in a biofilm. While cheater strains have been proposed as a control strategy to disrupt the harmful cooperative biofilm, some yeast strains cooperate only with other cooperators via kin recognition. We study under what circumstances kin recognition confers the greatest fitness benefit to a cooperative strain. Finally, we look at a multiscale, two-patch model for the dynamics between wild-type (WT) poliovirus and defective interfering particles (DIPs) as they travel between organs. DIPs are non-viable variants of the WT that lack essential elements needed for reproduction, causing them to steal these elements from the WT. We investigate when DIPs can lower the WT population in the host.

This dissertation unravels intricate biological dynamics in three distinct biological systems as the following. These studies combine mathematical models with experimental data to enhance our understanding of these complex processes. 1. Bipolar Spindle Assembly: Mitosis relies on the formation of a bipolar mitotic spindle, which ensures an even distribution of duplicated chromosomes to daughter cells. We address the issue of how the spindle can robustly recover bipolarity from the irregular forms caused by centrosome defects/perturbations. By developing a biophysical model based on experimental data, we uncover the mechanisms that guide the separation and/or clustering of centrosomes. Our model identifies key biophysical factors that play a critical role in achieving robust spindle bipolarization, when centrosomes initially organize a monopolar or multipolar spindle. These factors encompass force fluctuations between centrosomes, balance between repulsive and attractive inter-centrosomal forces, centrosome exclusion from the cell center, proper cell size and geometry, and limitation of the centrosome number. 2. Chromosome Oscillation: During mitotic metaphase, chromosomes align at the spindle equator in preparation for segregation, and form the metaphase plate. However, these chromosomes are not static; they exhibit continuous oscillations around the spindle equator. Notably, either increasing or decreasing centromeric stiffness in PtK1 cells can lead to prolonged metaphase chromosome oscillations. To understand this biphasic relationship, we employ a force-balance model to reveal how oscillation arises in the spindle, and how the amplitude and period of chromosome oscillations depend on the biological properties of spindle components, including centromeric stiffness. 3. Pattern Formation in Bacterial-Phage Systems: The coexistence of bacteriophages (phages) and their host bacteria is essential for maintaining microbial communities. In resource-limited environments, mobile bacteria actively move toward nutrient-rich areas, while phages, lacking mobility, infect these motile bacterial hosts and disperse spatially through them. We utilize a combination of experimental methods and mathematical modeling to explore the coexistence and co-propagation of lytic phages and their mobile host bacteria. Our mathematical model highlights the role of local nutrient depletion in shaping a sector-shaped lysis pattern in the 2D phage-bacteria system. Our model further shows that this pattern, characterized by straight radial boundaries, is a distinctive indicator of extended coexistence and co-propagation of bacteria and phages. Such patterns rely on a delicate balance among the intrinsic biological characteristics of phages and bacteria, which have likely arisen from the coevolution of cognate pairs of phages and bacteria. / Doctor of Philosophy / Mathematical modeling is a powerful tool for studying intricate biological dynamics, as modeling can provide a comprehensive and coherent picture about the system of interest that facilitates our understanding, and can provide ways to probe the system that are otherwise impossible through experiments. This dissertation includes three studies of biological dynamics using mathematical modeling: 1. Bipolar Spindle Assembly: Mitotic spindle is a bipolar subcellular structure that self-assembles during cell division. The spindle ensures an even distribution of duplicated chromosomes into two daughter cells. Certain perturbations can cause the spindle to assemble abnormally with one pole or more than two poles, which would cause the daughter cells to inherit incorrect number of chromosomes and die from the error. However, the cell is surprisingly good at correcting these spindle abnormalities and recovering the bipolar spindle. Here we build a model to explore how the cell achieves such recoveries and preferentially form a bipolar spindle to rescue itself. 2. Chromosome Oscillation: In mitotic metaphase, chromosomes are aligned at the spindle equator before they segregate. Interestingly, unlike the cartoon images in textbooks, the aligned chromosomes often move rhythmically around the spindle equator. We used a mathematical model to unravel how the chromosome oscillation arises and how it depends on the biological properties of the spindle components, such as stiffness of the centromere, the structure that connects the two halves of duplicated chromosomes. 3. Pattern Formation in Bacterial-Phage System: Phages are viruses that hijack their host bacteria for proliferation and spreading. In this study we developed a mathematical model to elucidate a common lysis pattern that forms when expanding host bacterial colony encounters phages. Interestingly, our model revealed that such a lysis pattern is a telltale sign that the bacterium-phage pair have achieved a delicate balance between each other and are capable of spreading together over a long period of time.

No description available.

No description available.